The problems under consideration center around the interpretation of binocular stereo disparity. In particular, the goal is the establish a set of mappings from stereo disparity to corresponding three dimensional scene sgeometry. Stereo disparity is represented as a vector field derived from differential projection of a three dimensional scene onto a pair of two- dimensional imaging surfaces. The resulting disparity field is analyzed with the aid of mathematical tools from classical field theory. This analysis analysed with the aid of mathematical tools from classical field theory. This analysis shows how disparity information can be interpreted in terms of three dimensional scene properties, such as surface depth, discontinuties and orientation. These theoretical developments have been embodied in a set of computer algorithms for the recovery of scene geometry from input stereo disparity. The results of applying these algorithms to several disparity maps are presented. Finally, comparisons are made to the interpretation of stereo disparity by biological systems. Keywords: Image understanding; Stereo images; Surface representation; Three Dimensional vision; Theses.